Where Pt is inflation, Yt is output, E[Pt] is expected inflation, and Xt is some exogenous variable.

The structural parameter b is the slope of the Short Run Phillips Curve, holding expected inflation constant. And the slope of the Long Run Phillips Curve, where actual equals expected inflation, is infinite. (If you prefer, you can replace Yt with -Ut, where Ut is the unemployment rate, so that -b is the slope of the Short Run Phillips Curve).

In this model, by construction, the slope of the Phillips Curve is fixed. In this model, inflation targeting cannot make the Phillips Curve really flatter. Nothing can make the Phillips Curve really flatter.

But inflation targeting can make the Phillips Curve look flatter.

There are two ways that inflation targeting can make the Phillips Curve look flatter.

1. Inflation targeting tries to make expected inflation constant.

If both actual inflation and expected inflation vary, and if the two are positively correlated (which they would be unless inflation were totally unpredictable or people had totally irrational expectations), then any observed correlation between Pt and Yt would be some sort of average of the Short Run and Long Run Phillips Curves. To the extent that inflation targeting succeeds in making expected inflation constant, we would only observe the Short Run Phillips Curve and never observe the Long Run Phillips Curve. Since the SRPC is flatter than the LRPC, if inflation targeting made expected inflation more constant it would make the Phillips Curve look flatter.

2. Inflation targeting tries to make actual inflation constant.

Assume that inflation targeting succeeds in making expected inflation constant. The observed correlation between Pt and Yt will depend on whether the exogenous variable Xt is correlated with Yt.

If Xt and Yt are uncorrelated, we will observe a positive correlation between Pt and Yt, with a slope equal to the structural parameter b. We would observe the Short Run Phillips Curve, plus random noise.

But inflation targeting will try to make Xt and Yt perfectly negatively correlated. To keep inflation perfectly on target, the central bank would need to adopt a monetary policy that ensured that Yt=-(1/b)Xt.

If Xt and Yt are negatively correlated, the observed correlation between Pt and Yt would have a slope less than b. If the central bank had a crystal ball, and kept inflation perfectly on target, the Phillips Curve would look perfectly flat, because Yt would vary but Pt would stay constant.

3. Putting both 1 and 2 together: the better the central bank is at targeting inflation, the flatter the Phillips Curve will look, even though it doesn't make it really flatter.

If econometricians could observe E(Pt) and Xt, they could estimate equation 1 and estimate the parameter b directly. They could eliminate the omitted variable bias that comes from looking at simple regressions when multivariate regressions are appropriate. If they saw that b became smaller after central banks started targeting inflation, that could help us understand why inflation targeting failed.

Now econometricians might have some information on E(Pt) and Xt, that they could use when estimating equation 1. But it is unlikely they will observe E(Pt) and Xt without error. So we get errors in variables bias, unless the observation errors in E(Pt) and Xt are uncorrelated with Yt, which will probably not be the case. Because remember: the whole point of inflation targeting is to make the Phillips Curve look flat, and the way to make the Phillips Curve look flat is to make Yt perfectly negatively correlated with E(Pt) and Xt.

I think we need some other sort of evidence if we want to find out if inflation targeting made the Phillips Curve really flatter.

You're saying modern central banks respond to AS expansion by expanding AD in response and reducing AS by reducing AD in response?

1. Is that consistent with a central bank that keeps the LM curve vertical?

2. Say 'endogenous trend' is 2% inflation, 3% real growth. AS expands, pushing the constant AD split to 1% inflation and 4% growth. Now to keep inflation at 2%, the CB expands AD. Unless the *actual* AS curve is vertical, this will mean real growth in excess of 4%, say 5%. So real GDP growth swings from 3% to 5%. And sometimes from 3% to 1%. Without asking for prrofs, does your reading of the real GDP data suggest this may be the case?

1. Yes. It tries to keep the LM curve vertical at that level of output that which is consistent with 2% forecast medium term inflation, which is a moving target. So it shifts the LM curve right or left if it thinks Xt has changed. But it doesn't let IS shocks (at least, those it sees) change Yt, so the LM is vertical.

2. If some real shock causes the LRAS shift right by (say) 1% (relative to trend), will that same real shock also cause the SRAS curve to shift right by the same 1% (relative to its trend)? That depends on the model, and on the nature of the shock. My sense from the data is that it does not always cause SRAS and LRAS to shift right by the same amounts. There are shocks that cause SRAS to shift a lot more than LRAS. We sometimes call them "price shocks", though that is a very bad name ("never reason from a price change")

Nick, is this idea related to your paper on "Why U.S. money does not cause U.S. output, but does cause Hong Kong output"? That perfect offsetting of shocks removes the relationship between money (or, in this case, inflation) and output in the US, but the effect of monetary policy is still felt somewhere, perhaps in another country?

b: A lot of other bloggers seem to be covering Reinhardt and Rogoff. And I hadn't even read the original R&R paper (though I had heard about it). So I don't have anything useful to add to the conversation.

While its true that targeting inflation failed to prevent a big drop if RGDP in 2008 I am not sure that there is much evidence that this happened because IT "destroyed the usefulness of inflation as a signal of whether money should be tightened or loosened". I think it more likely that there are simply some scenarios that IT could never deal with and it was just lucky that these scenarios never came around until 2008.

With a CB expecting 3% real growth and targeting inflation of (say) 2% then it can pick up small variations in inflation expectations , make the necessary adjustments to the money supply, hit the inflation target and keep RGDP on track.

A huge fall in business confidence (like we saw in 2008) could in the short term so affect the relative prices that would be needed for full employment that it would be possible to hit the inflation target even with RGDP falling. For example: Investment plans are cut back leading to a fall in the demand for labor but sticky wages prevent them falling to the levels that would clear the labor markets. IT leads to the money supply increasing to prevent deflation but not to allow the adjustments to real wages needed to maintain RGDP.

NGDPT by preventing nominal spending from falling will fair better but if the fall in confidence is severe enough then wage level targeting (that would allow the price level to rise until real wages are at the correct level) would be better still, assuming with either of these regimes that the higher level of inflation generated does not have a further negative effect on business confidence.

Ron: I would re-word what you said as: "A huge fall in business confidence (like we saw in 2008) could in the short term so affect the relative prices that would be needed for full employment that it would be IMpossible to hit the inflation target [] withOUT RGDP falling."

That's what you meant, right?

OK. So there are two theories about why IT failed: 1. my "IT made the PC too flat"; 2. your "IT can't handle a relative price shock that shifts the PC up".

I think those two theories are complements rather than substitutes. The flatter the PC, the worse IT will fail if a relative price shock shifts the PC up. In the limit, as the SRPC becomes perfectly flat, IT means that the tiniest upward shift to the SRPC causes a massively big recession.

Suppose that we arrived at the exact same situation as in 2008 but after 20+ years of ad-hoc target-free CB policy rather than IT. What would have happened if the CB had increased the money supply by the same amount that they did to hit the inflation target ? Most likely (but not for sure) RGDP would have ended up higher with ad-hoc compared to IT. The reason would indeed be that the Phillips curve would have been steeper in the ad-hoc world. (It is possible that under ad-hoc CB policy things may have been worse - in the absence of an inflation target people may have feared deflation and reduced expectations further.)

In the face of an extreme demand shock IT will 1) reduce the effectiveness on policy by flattening the PC and 2) Reduce the scope of policy by restricting it to hitting the target. Against this it is likely that in "normal" times IT optimizes RGDP growth so the "great recession" started from a much higher peak than it otherwise would have.

I don't really think IT can be blamed for the 2008 demand(expectations?)-shock. But the weaknesses of IT was badly exposed by it. NGDPT seems to suffer from some of the same weaknesses as IT - It may not be possible to optimize RGDP growth while hitting the target. I think Wage LT (perhaps bounded by an upper inflation condition) may be the optimum. It gives a stable framework for for normal times and flexibility for extreme times. It also allows the CB to exploit the SRPC by making inflation expectations unpredictable especially in a deep recession.

On "But I wish we could find good evidence to test them." : Since when did economists let the facts stand in the way of a good theory ?

At one time the powers that be thought that they could "buy down" un-employment at the cost of a little inflation. The model rebeled. They revised model was to say that the Philips curve is vertical.

Then the powers that be decided that if they couldn't make unemployment behave, they would make inflation behave. It does not surprize me in the least that this would cause the Philips curve to be horizontal!

I'm wondering if the econometric problems you identify might be alleviated by looking at the behaviour of prices at the level of individual industries. Even if CB policy tries to make "Yt perfectly negatively correlated with E(Pt) and Xt" at the aggregate level, much of the variation in industry-level Yt (deviation of industry output/employment from trend, some measure of industry-spcific capacity utilization) will reflect industry-specific factors. The point is that if IT has in fact made prices less responsive to deviations from "full employment", this should also show up at industry-level even when the deviations in question are the result of industry-specific rather macro shocks. (Or have I misunderstood your hypothesis?)

I have to note an even simpler expanation. The Phillips curve is a curve. In Phillips's data for anchored inflation (pre 70s indeed pre 60s) equation one is rejected. The Phillips curve was convex so the slope was low for low inflation rates.

I think this is an absolutely fair critique of the IMF research paper which asserts that the Phillips curve has changed. It is only valid analysis if by "curve" means "straight line"

Long before any systematic thought about expectatiions, Phillips, Samuelson and Solow could have predicted that the slope of inflation with respect to Y would be low at low inflation rates.

In the available data, successfully targeted inflation and low inflation occur mostly at the same times and places.

Your story is interesting, but it can only be distinguished from the curves curve hypothesis is there is an episode of inflation targeting with a high target or an episode of unsuccessfully targeted but low inflation . There has not yet been a high inflation target, so the (post Phillips) example would have to be Japan where inflation has been very low and under target often over the past two decades. The Japanese Phillips curve is flat. The result is more nearly low inflation implies low slope not successful targeting implies a low slope.

Note the original Phillips curve as graphed by Phillips generally showed a low slope at low inflation rates http://en.wikipedia.org/wiki/Phillips_curve

There were two years of sharp deflation, one of -3% and 11 (of 36 in the scatter graph I am eyeballing) with inflation from -2% to +2% and unemployment from 10 % to 22%.

A flat Phillips curve at low inflation rates is not a new phenomenon which occured after monetary authorities learned how to successfully target inflation. Phillips's data set also includes a year with nominal wage inflation of 32%.

Doug M: Yep, looking back on history, it seems we have gone from one extreme (targeting output/unemployment) to the other extreme (targeting inflation). NGDP targeting seems like a sensible middle ground.

Giovanni: I'm not sure whether that would work. IT might also have made industry-specific Phillips Curves really flatter and/or look flatter.

Robert: good comment. Yes, a curved PC that is flatter at low inflation would be yet another theory of why IT failed. "IT would have worked fine if they had targeted a higher rate of inflation where the Phillips Curve is steeper!" (Would we model that by making b a positive function of E(P)?) But that too is rather hard to test, since I think we would need examples of IT countries with higher inflation targets. And even if we had such examples, the Phillips Curve might still look flat, even if it wasn't really flat, for the reasons I have given above.

Canadian Content: Let's add Richard Lipsey's name to your list, because Lipsey was one of the very first to put forward a theoretical explanation of the early Phillips Curve, and he has always insisted it is curved and not straight.

I wrote this post partly in response to that recent IMF research. But I was rushed when writing it, and couldn't find the link.

Ron Ronson said: "I think it more likely that there are simply some scenarios that IT could never deal with and it was just lucky that these scenarios never came around until 2008."

Would going from supply constrained to demand constrained be a scenario?

"A huge fall in business confidence (like we saw in 2008)..."

I'd say businesses attempt to predict quantities, and in 2008 they correctly predicted quantities were going to go down.

"For example: Investment plans are cut back leading to a fall in the demand for labor but sticky wages prevent them falling to the levels that would clear the labor markets."

I usually find sticky wages (or sticky prices) lead to discussions about shortages of medium of account (MOA)/medium of exchange (MOE). Sticky currency denominated debt could be involved too.

"NGDPT by preventing nominal spending from falling will fair better but if the fall in confidence is severe enough then wage level targeting (that would allow the price level to rise until real wages are at the correct level) would be better still, ..."

That sounds to me like you want to lower real wages. What if real wages being too low led to the recession?

on "That sounds to me like you want to lower real wages. What if real wages being too low led to the recession?"

I had in mind a model where the equilibrium wage level for full employment had fallen and inflation could be used to reduce real wages. I understand that other models see the wage level as a key component of AD. If that is true then I suppose that targeting NGDP would always be enough to maintain full employment.

"I had in mind a model where the equilibrium wage level for full employment had fallen and inflation could be used to reduce real wages."

I don't believe that is what is happening now. If that was so, I think there should be shortages leading to price inflation and corporate profit as a % of GDP should be below average not at record highs or near record highs.

"Record quarterly earnings. That's right. Record. First-quarter earnings for the S&P 500 currently stand at $26.44, according to S&P Capital IQ, the highest ever for a single quarter, beating the prior record of $26.36 for the fourth quarter of 2012."

"The big story this quarter, as I have repeatedly emphasized, has been the revenue misses, with only 43 percent of companies reporting beating on the top line.